The deformation equation and its integrability condition (Bianchi identity) of a non-associative deformation in operad algebra are found. Their relation to the theory of gravity is discussed.

We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized by H(S,R). The fuzzy sphere is included as a special case parametrized by the integer two-cohomology class H(S,Z), which has finite number of degrees of fre...

We customize here, for the purposes of precomputed and interactive deformation and animation techniques, some basic concepts and deformation methods of differential topology related to Cobordism Theory.

The deformation of an object is the result of a process. According to the current trends in engineering surveying, the analysis of deformations intends to figure out the dynamics of this process. Apart from the geometrical changes observed, the basis of the investigations is to incorporate the causative forces and the physical properties of the body. In its entirety, the body, the influencing f...

Using a combination of explicit solvent atomistic simulation and continuum theory, here we study the lateral deformation mechanics of three distinct protein structures: an amyloid fibril, a beta helix, and an alpha helix. We find that the two β-sheet rich structures - amyloid fibril and beta helix, with persistence lengths on the order of μm - are well described by continuum mechanical theory, ...

We investigate deformed Wess-Zumino model on N = 1 four dimensional superspace in which bosonic-fermionic noncommutativitiy [x, θ] = iλ is realized. This deformation intertwines ordinary space-time noncommutative field theory and recently proposed N = 1 2 non-(anti)commutative theory. This deformation is nilpotent and we can explicitly evaluate noncommutative effect by means of new interaction ...

We develop the deformation theory of A∞ algebras together with∞-inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation theories of associative algebras, A∞ algebras, associative algebras with inner products, and A∞ algebras with inner products.

We construct a universal envelope for any Poissonand Gerstenhaber algebra. While the deformation theory of Poisson algebras seems to be partially trivial, results from string and M -theory suggest a rich deformation theory of Gerstenhaber algebras. We apply our construction in this case to well known questions on the topological closed string BRST-complex. Finally, we find a simliar algebraic s...

In this paper we show that the number of deformation types of complex structures on a fixed smooth oriented four-manifold can be arbitrarily large. The examples that we consider in this paper are locally simple abelian covers of rational surfaces. The proof involves the algebraic description of rational blow down, classical Brill-Noether theory and deformation theory of normal flat abelian covers.

This paper describes a method based on metric structures for anatomical analysis on a large set of brain MR images. A geodesic distance between each pair was measured using large deformation diffeomorphic metric mapping (LDDMM). Manifold learning approaches were applied to seek a low-dimensional embedding in the highdimensional shape space, in which inference between healthy control and disease...